1. What is Harmonic Mean?

The harmonic mean is a type of average that is appropriate for situations when the average of rates is desired. It is particularly useful for rates, ratios, and other situations where the average of reciprocals is meaningful.

2. How Does the Calculator Work?

The calculator uses the harmonic mean formula:

Where:

• \( n \) — Number of elements
• \( x_i \) — Each individual value in the set

Explanation: The harmonic mean is calculated by dividing the number of observations by the sum of reciprocals of each observation.

3. When to Use Harmonic Mean

Details: The harmonic mean is especially useful when dealing with rates, ratios, or situations where you need to give equal weight to each data point's contribution to the average.

4. Using the Calculator

Tips: Enter numbers separated by commas. All values must be positive numbers (cannot be zero). The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: When should I use harmonic mean instead of arithmetic mean?
A: Use harmonic mean when averaging rates (like speed) or ratios where you want to give equal weight to each data point's contribution.

Q2: What are common applications of harmonic mean?
A: Common uses include calculating average speed, average fuel economy in miles per gallon, and financial ratios like price-earnings ratios.

Q3: Why can't the harmonic mean handle zero values?
A: Because the harmonic mean involves reciprocals, and division by zero is undefined. Any zero in the dataset makes the harmonic mean undefined.

Q4: How does harmonic mean compare to other averages?
A: For any dataset with positive numbers, harmonic mean ≤ geometric mean ≤ arithmetic mean.

Q5: Can harmonic mean be used with negative numbers?
A: No, harmonic mean is only defined for positive real numbers.